Anosov representations and proper actions

François Guéritaud, Olivier Guichard, Fanny Kassel, Anna Wienhard

Published 2015-02-12Version 1

We give several new characterizations of Anosov representations of word hyperbolic groups into real semisimple (or more generally reductive) Lie groups, in terms of a Cartan projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of reductive groups. We describe explicit compactifications of the resulting (noncompact) quotient manifolds.